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diffraction data provided an excellent fit to the
structural model (table S3), confirming an ef-
ficient self-healing with retention of high struc-
tural integrity and precise alignment of the
broken pieces (see tables S2 to S5 and figs. S7,
S16, and S17). It is noteworthy that although
the long-range structural order of bulk single
crystals can be captured well by SCXRD, the
nanoscale structural inhomogeneities (if any)
are not revealed because of the averaging na-
ture of the technique. On the other hand, an
imperfectly healed crystal with a visible crack
showed sharp but doubly split diffraction
peaks, revealing the misalignment of the two
well-ordered crystalline macroscopic domains
(Fig. 3E and fig. S16).
Using a custom designed state-of-the-art
dark-field Mueller matrix microscopy system
(fig. S18) with maximum spatial resolution of
~300 nm ( 23 ), we quantified the healing effi-
ciency by measuring the microscopic aniso-
tropic order of the crystals, including at the
crack junction (Fig. 4 and figs. S19 and S20).
Using the Mueller matrix, which encodes the
full polarization response of the interacting
medium, one can efficiently probe and quan-
tify the anisotropic polarizability of crystalline
or other ordered materials using suitable com-
binations of polarization states of light ( 23 , 24 ).
The important linear anisotropy parameters
in this context are the magnitude of linear
retardance (dL, birefringence), the orientation
angle of the retarder (q, birefringence axis),
and linear diattenuation (dL)( 23 , 24 ). The mea-
sured values ofdLanddLprovide quantitative
measures of the order parameters.
Pristine crystals, with a high degree of local
order, showed strong phase and amplitude
anisotropy effects, resulting in the highest
magnitudes of anisotropic parameters (dL=
1.52 ± 0.16 rad anddL=0.209±0.003)(Fig.4,
AtoC).Theneatlyhealedcrystalsalsoshowed
an impressive internal order, with only a slight
decrease in parameters (dL=1.34±0.1radand
dL= 0.189 ± 0.005) (Fig. 4, D to F, and fig. S20).
This quantifies the self-healing efficiency in
the neatly healed crystals of 1 as 88%. In the
context of nanoscale order, our technique cap-
tures any imperfections more efficiently than
the macroscopic imaging or SCXRD techniques
( 8 , 9 ). Samples obtained by fragmenting a crys-
tal into multiple pieces also showed order com-
parable to that of the neatly healed crystals
(figs. S21 and S22 and tables S7 and S8). This
confirms that the mechanical impact perma-
nently decreases the overall structural order
by 10 to 15%, leading to introduction of some
permanent defects in the crystals ( 18 , 19 ). We
propose that this strain leads to a slight im-
balance of dipoles in the polar crystals, result-
ingintheremnantsurfacechargesonthe
fractured faces, as evidenced from KPFM data.
Defects formed by doping are also known to
create polar domains due to lowering of sym-


metry in centrosymmetric crystals ( 25 ). None-
theless, the slight decrease in the microscopic
orientation of the axis of the retarder (com-
pare arrows in Fig. 4, C and F) is evident for
the neatly healed versus pristine crystals. How-
ever, the highly ordered, nanoscopically re-
paired nature of the neatly healed crystals is
apparent from our results.
In the case of imperfectly healed crystals with
visible cracks, a large decrease in the param-
eters is seen (dL=0.70±0.1radanddL= 0.07 ±
0.008; Fig. 4G and figs. S21 and S22). This find-
ing suggests the misalignment of local aniso-
tropic domains, which decreases the order
parameters by ~50%. Nanoscale spatial varia-
tion of the order parameters for the imperfectly
healed crystal shows the drop of order at the
crack line or imperfectly healed junction,
whereas the neatly healed crystals showed
no noticeable variations in the healed region
(Fig. 4, E and H). This indicates that the neatly
healed crystals not only retain near-maximum
overall long-range crystalline order but also
successfully heal and reknit the fragments
with nanoscale precision, which is highly
desirable for technology applications, particu-
larly in deployment of piezoelectric materials
in precision applications such as transducers.
This piezoelectricity-based repair mechanism
can be transferred to other polar materials
such as semicrystalline films retaining order
at nanoscale, which would be more amenable
to technology transfer.
The significant drop in the anisotropic order
parameters in imperfectly healed crystals as
compared to neatly healed crystals (tables S6
to S8) suggests that the inefficient healing has
a penalty on the structural order, leading to
enhanced residual stress and surface charges
in the crystal. This is consistent with the ob-
served residual partial charges across the crack
line in the KPFM data. Hence, achieving align-
ment of the pieces with crystallographic precision
appears to be more favorable so as to avoid the
penalty associated with remnant charges on the
crystal.
To better understand and benchmark the
self-healing potential of our molecular crystals,
we performed control experiments on some
readily available centrosymmetric (nonpiezo-
electric) and noncentrosymmetric (piezoelectric)
crystals (figs. S23 to S27 and table S9). A known
nonpiezoelectric hemihydrate crystal (space
groupI 41 /acd) of the same bipyrazole mole-
cule in 1 exhibited neither attraction between
broken pieces nor any self-healing upon frac-
ture. Nonpiezoelectric crystals, because of their
centrosymmetric structure, cancel the dipoles,
hence they are not ideal for developing net
charges on fracture surfaces. Some well-known
piezoelectric amino acid crystals,g-glycine and
L-histidine, with similar needle morphologies,
also did not show any self-healing, which sug-
gests that piezoelectric nature alone is not a

sufficient condition. These crystals, with pre-
dominantly strong hydrogen-bonding networks
and minimally dispersive types of interactions,
are very stiff (high elasticity), hence less prone to
plastic deformation ( 18 ). They did not show any
sign of attraction between the fracture surfaces.
As positive controls, confirming the identified
design principles of noncentrosymmetry and
crystal packing for favoring some degree of
plastic deformation, slender needle-like piezo-
electric crystals of some other organic com-
pounds (named as crystals 2 , 3 , 4 , and 5 )
exhibited interparticle attraction and excep-
tional self-healing behavior comparable to
that seen in crystals of 1 (see figs. S23 to S27
and table S9 for more details).
Noncentrosymmetric molecular crystals, owing
to their piezoelectric nature, develop opposite
charges on strained fracture surfaces, prompt-
ing fast recombination of the fragments, even
when they are not in direct contact, and show
autonomous self-healing with high crystallo-
graphic precision. Piezoelectric molecular crys-
tals can be readily accessed from a large number
of the well-known enantiomerically pure natural
and synthetic compounds; in particular, those
with (but not limited to) dispersive functional
groups would be appropriate for exploring the
self-healing property. One may use the crystal
structure databases for mining potential can-
didates with noncentrosymmetric space groups
and desired crystal packing features, and to
further develop new self-healing materials
using crystal engineering principles ( 21 , 22 , 26 ).

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